1 // Special functions -*- C++ -*-
3 // Copyright (C) 2006-2018 Free Software Foundation, Inc.
5 // This file is part of the GNU ISO C++ Library. This library is free
6 // software; you can redistribute it and/or modify it under the
7 // terms of the GNU General Public License as published by the
8 // Free Software Foundation; either version 3, or (at your option)
11 // This library is distributed in the hope that it will be useful,
12 // but WITHOUT ANY WARRANTY; without even the implied warranty of
13 // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
14 // GNU General Public License for more details.
16 // Under Section 7 of GPL version 3, you are granted additional
17 // permissions described in the GCC Runtime Library Exception, version
18 // 3.1, as published by the Free Software Foundation.
20 // You should have received a copy of the GNU General Public License and
21 // a copy of the GCC Runtime Library Exception along with this program;
22 // see the files COPYING3 and COPYING.RUNTIME respectively. If not, see
23 // <http://www.gnu.org/licenses/>.
25 /** @file tr1/poly_hermite.tcc
26 * This is an internal header file, included by other library headers.
27 * Do not attempt to use it directly. @headername{tr1/cmath}
31 // ISO C++ 14882 TR1: 5.2 Special functions
34 // Written by Edward Smith-Rowland based on:
35 // (1) Handbook of Mathematical Functions,
36 // Ed. Milton Abramowitz and Irene A. Stegun,
37 // Dover Publications, Section 22 pp. 773-802
39 #ifndef _GLIBCXX_TR1_POLY_HERMITE_TCC
40 #define _GLIBCXX_TR1_POLY_HERMITE_TCC 1
42 namespace std _GLIBCXX_VISIBILITY(default)
44 _GLIBCXX_BEGIN_NAMESPACE_VERSION
46 #if _GLIBCXX_USE_STD_SPEC_FUNCS
47 #elif defined(_GLIBCXX_TR1_CMATH)
51 # error do not include this header directly, use <cmath> or <tr1/cmath>
53 // [5.2] Special functions
55 // Implementation-space details.
59 * @brief This routine returns the Hermite polynomial
60 * of order n: \f$ H_n(x) \f$ by recursion on n.
62 * The Hermite polynomial is defined by:
64 * H_n(x) = (-1)^n e^{x^2} \frac{d^n}{dx^n} e^{-x^2}
67 * @param __n The order of the Hermite polynomial.
68 * @param __x The argument of the Hermite polynomial.
69 * @return The value of the Hermite polynomial of order n
72 template<typename _Tp>
74 __poly_hermite_recursion(unsigned int __n, _Tp __x)
87 _Tp __H_n, __H_nm1, __H_nm2;
89 for (__H_nm2 = __H_0, __H_nm1 = __H_1, __i = 2; __i <= __n; ++__i)
91 __H_n = 2 * (__x * __H_nm1 - (__i - 1) * __H_nm2);
101 * @brief This routine returns the Hermite polynomial
102 * of order n: \f$ H_n(x) \f$.
104 * The Hermite polynomial is defined by:
106 * H_n(x) = (-1)^n e^{x^2} \frac{d^n}{dx^n} e^{-x^2}
109 * @param __n The order of the Hermite polynomial.
110 * @param __x The argument of the Hermite polynomial.
111 * @return The value of the Hermite polynomial of order n
114 template<typename _Tp>
116 __poly_hermite(unsigned int __n, _Tp __x)
119 return std::numeric_limits<_Tp>::quiet_NaN();
121 return __poly_hermite_recursion(__n, __x);
123 } // namespace __detail
124 #if ! _GLIBCXX_USE_STD_SPEC_FUNCS && defined(_GLIBCXX_TR1_CMATH)
128 _GLIBCXX_END_NAMESPACE_VERSION
131 #endif // _GLIBCXX_TR1_POLY_HERMITE_TCC